By J. G. A. Bitter (auth.)
The current publication incorporates a comparability of latest theoretical versions constructed on the way to describe membrane separation strategies. mostly, the permeation equations caused by those versions provide misguided predictions of the mutual results of the permeants concerned, as a result of the simplifications followed of their derivation. it really is concluded that an optimal description of delivery phenomena in tight (diffusion-type) membranes is accomplished with the "solution-diffusion" version. in keeping with this version every one component to a fluid blend to be separated dissolves within the membrane and passes via by way of diffusion based on its gradient within the chemical strength. A transformed Flory-Huggins equation has been derived to calculate the solubility of the permeants within the membrane fabric. opposite to the unique Flory-Huggins equation, the transformed equation debts for the massive impression on solubility of crystallinity and elastic pressure of the polymer chains through swelling. The equilibrium sorption of beverages computed with this equation was once stumbled on to be in sturdy contract with experimental effects. additionally, the sorption of gases in either rubbery and glassy polymers can be defined quan titatively with the transformed Flory-Huggins equation with none want of the arbitrary Langmuir time period, as required within the traditional "dual-mode" sorption version. additionally, fewer parameters are required than with the at the very least exact accuracy.
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Sample text
9), yields the modified Maxwell-Stefan (MMS) equation: *D. L... 11 ) J=1 j#i In the derivation of this equation no arbitrary assumption for the average friction has been introduced, as was done in the derivation of the MS Eq. 4), and therefore the former has a more general validity. Another advantage of the MMS equation is that the diffusivity is expressed explicitly, which enhances its accessibility and facilitates its practical applicability. For predicting *D im a suitable model is still required.
Cbi Retentate ,Laminar ! 19) in which k; = Djo is the mass transfer coefficient. Correspondingly, such an equation can be derived for eventual concentration polarization effects at the permeate side of the membrane. According to Eq. 19) the concentration of the retained component at the membrane interface increases with respect to its concentration in the bulk phase if the ratio of the total flux and the mass transfer coefficient increases, thus reducing the concentration gradient across the membrane of the component to be separated, and hence its flux.
4 ) j#; in which Dij is the binary Maxwell-Stefan (MS) diffusivity of i in a mixture of i andj. In order to derive this equation it was tacitly assumed that D ij is independent of concentration and of the presence of other components (see Appendix III). In the case of gases, for which the diffusivities usually show only minor differences, Eq. 4) can be applied successfully. For mixtures of liquids 56 and of polymers and liquids, 4 however, it has been observed experimentally that D ij varies considerably with composition and concentration, although much less than Fickian.